1. Field of the Invention
The present invention generally relates to systems and methods for designing reflectors and, more particularly, to a system and method for designing a free form reflector.
2. Description of Related Art
Non-imaging reflectors are widely used in illumination and solar energy systems. In these applications, a non-imaging reflector is designed to convert the Lambertian source into a beam with a divergence of half-angle θ without loss of throughput. One direct design approach is to using algebraic methods, among which a tailored edge ray approach has made a great success. In this approach, a two-dimensional (2D) reflector is determined by reflector equations that are deduced from an edge-ray method and conservation of energy. For a three dimensional (3D) reflector design, it is common to solve the problem by reducing three dimensions to two dimensions. Thus, a 3D reflector can be generated by means of rotational or translational symmetry. The second approach is indirect, and it uses optimization-based design techniques. The analytic knowledge of the connection between the reflector structure and optical performance is not needed. Free form surfaces, such as a Bézier surface and a non-uniform rational basis splines (NURBS) surface, are appropriate to represent the shape of a reflector in these automated design approaches.
A genetic algorithm has been proven to be valuable both in imaging and non-imaging optics since Holland laid down the basic principles of genetic algorithms. A differential evolution (DE) is a variation of the genetic algorithm proposed by R. Storn and K. Price. The DE stood out in the first IEEE conference on evolutionary computation, and then it was widely applied in various fields. Compared with standard the genetic algorithm, the DE uses floating point variables. In addition, the crossover and mutation implementations are more complex. The NURBS is a powerful technique for constructing general curves and surfaces. It has many good properties, for example, the order of the surface is independent of the number of control points. Local changes to the surface shape are possible because individual control points have only local influences. The algorithm combines the global search capability of the DE with the flexibility of the shape adjustment of free form surface, which has been used in the second approach of reflector design. S. Doyle used cubic Bézier curve to represent the profile of a reflector, and thus a paraboloid and ellipse reflector can be obtained by using his algorithm.
For the design of a non-imaging reflector, what is needed is a system and method for designing a free form reflector that performs an automated free form reflector generation, which can be applied for the design of more general reflectors.